1. Field of the Invention
The present invention relates generally to modelocking, and in particular, to cw modelocking in which Q-switched pulses are suppressed.
2. Description of the Related Art
Semiconductor saturable absorbers have recently found application in the field of passively modelocked, ultrashort pulse lasers. These devices are attractive since they are compact, inexpensive, and can be tailored to a wide range of laser wavelengths and pulsewidths. Semiconductor saturable absorbers were first used to passively modelock a diode laser (see P. W. Smith, Y. Silberberg and D. B. A. Miller, "Mode locking of semiconductor diode lasers using saturable excitonic nonlinearities," J. Opt. Soc. Am. B, vol. 2, pp. 1228-1236, 1985 and U.S. Pat. No. 4,435,809 to Tsang et al). Quantum well and bulk semiconductor saturable absorbers have also been use d to modelock color center (M. N. Islam, E. R. Sunderman, C. E. Soccolich, 1. Bar-Joseph, N. Sauer, and T. Y. Chang, "Color center lasers passively mode-locked by quantum wells", IEEE J. of Quantum Electronics, vol. 25, pp. 2454-2462 (1989)) and fiber lasers (U.S. Pat. No. 5,436,925 to Lin et al.).
A saturable absorber has an intensity-dependent loss 1. The single pass loss of a signal of intensity I through a saturable absorber of thickness d may be expressed as EQU l=1-exp(-.alpha.d) (1)
in which a is the intensity dependent absorption coefficient given by: EQU .alpha.(I)=.alpha..sub.0 /(1+I/l.sub.SAT) (2)
Here .alpha..sub.0 is the small signal absorption coefficient, which depends upon the material in question. I.sub.SAT is the saturation intensity, which is inversely proportional to the lifetime (.tau..sub.A) of the absorbing species within the saturable absorber. Thus, saturable absorbers exhibit less loss at higher intensity.
Because the loss of a saturable absorber is intensity dependent, the pulse width of the laser pulses is shortened as they pass through the saturable absorber. How rapidly the pulse width of the laser pulses is shortened is proportional to .vertline.dq.sub.0 /dI.vertline., in which q.sub.0 is the nonlinear loss: EQU q.sub.0 =1(I)-1(I=0) (3)
l(I=0) is a constant (=1-exp(-.alpha..sub.0 d)) and is known as the insertion loss. As defined herein, the nonlinear loss q.sub.0 of a saturable absorber decreases (becomes more negative) with increasing intensity 1. .vertline.dq.sub.0 /dl.vertline. stays essentially constant until I approaches I.sub.SAT, becoming essentially zero in the bleaching regime, i.e., when I&gt;&gt;I.sub.SAT.
For a saturable absorber to function satisfactorily as a modelocking element, it should have a lifetime (i.e., the lifetime of the upper state of the absorbing species), insertion loss l(I=0), and nonlinear loss q.sub.0 appropriate to the laser. Ideally, the insertion loss should be low to enhance the laser's efficiency, whereas the lifetime and the nonlinear loss q.sub.0 should permit self-starting and stable cw modelocking. The saturable absorber's characteristics, as well as laser cavity parameters such as output coupling fraction, residual loss, and lifetime of the gain medium, all play a role in the evolution of a laser from startup to modelocking.
To obtain rapid pulse shortening in a self-starting cw modelocked laser having a saturable absorber, the intensity on the saturable absorber should be high and the absorber should have a nonlinear loss q.sub.0 whose magnitude is large. On the other hand, reducing the loss of the saturable absorber causes the intracavity power to increase, which may lead to gain saturation. If the gain saturation does not dampen power increases caused by the large magnitude of the nonlinear loss q.sub.0, the laser ,will operate in a regime in which the laser Q-switches and modelocks simultaneously (~see H. A. Haus, "Parameter range for cw passive mode locking," IEEE, J. Quantum Electronics, QE-12, p. 169, 1976). This is particularly true for a laser medium with a very long lifetime such as an erbium-doped fiber (.tau..about.ms). Thus, to avoid Q-switching, the magnitude of the nonlinear loss q.sub.0 of the saturable absorber must be limited, but not to the point where self-staring of the modelocking becomes difficult. The insertion loss and the nonlinear loss q.sub.0 of a semiconductor saturable absorber can be controlled by selecting a material having the appropriate band gap and thickness.
The loss characteristics of a simple saturable absorber may be modified by the Fabry-Perot interference effect. Indeed, semiconductor saturable absorbers tend to form a natural Fabry-Perot structure since a semiconductor's relatively high index of refraction (typically 2-4) results in a semiconductor-air interface from which .about.10-40% of the incident light may be reflected. A semiconductor saturable absorber may have one side that is high reflection coated (e.g., for maximum reflectivity), with this high reflector forming one end of a laser cavity. In this case, the fraction R.sub.F-P of the intracavity power that is reflected from the semiconductor saturable absorber is given, by EQU R.sub.F-P =1-(1-R)(1-T)[1+RT+2(RT).sup.1/2 cos(2.delta.)].sup.-1 (4)
in which R is the front surface reflectivity of the saturable absorber (i.e., the reflectivity of the saturable absorber and any reflection coating thereon in the absence of reflection from the back side), .delta.=(2nd/.lambda.)2.pi. is the double pass phase change, d is the sample thickness, n is the index of refraction, and k is the wavelength of interest. T is the double pass transmission through the saturable absorber and is equal to exp(-2.alpha.d), with a being the absorption coefficient of the material. The corresponding absorption is then A1-T-1-exp(-2.alpha.d). If multiple layers with different indices of refraction and absorption coefficients are used as part of the Fabry-Perot etalon, equation (4) must be modified so that the double pass phase change and the absorption are summed over all the layers.
The fraction of the laser cavity power incident on the Fabry-Perot structure that is absorbed in the saturable absorber (F.sub.ABS) is in general not simply I-T, but rather 1-R.sub.F-P. This is due to the fact that a Fabry-Perot structure acts as a resonating structure, in which power may circulate before reentering the rest of the laser cavity.
According to equation (4), R.sub.F-P (the fraction of the intracavity standing power reflected from a semiconductor saturable absorber) is a sensitive function of the double pass phase change .delta., which depends upon the laser wavelength as well as the thickness and index of refraction of the saturable absorber. As illustrated in FIG. 1, for a given laser wavelength .lambda. and index of refraction n, the reflectivity of a Fabry-Perot device is a periodic function that depends upon the thickness d of the saturable absorber. If the thickness of the Fabry-Perot device is chosen to be d=.lambda.n/2n, in which m is a positive integer, the double pass phase change is .delta.=2m.pi., and the Fabry-Perot device is said to be at antiresonance. In this case, R.sub.F-P =1-(1-R)(1-T)[1+(RT).sup.1/2 ].sup.-2.
In addition to wavelength and thickness, R.sub.F-P can also be viewed as a function of R. FIG. 2 considers how R.sub.F-P varies as a function of R and wavelength .lambda. for a given saturable absorber thickness d. In particular, the higher R is, the more rapidly R.sub.F-P varies. When R=0 (i.e., when the surface of the saturable absorber that faces the gain medium is anti-reflection coated), R.sub.F-P =T and thus depends solely upon the absorption of the saturable absorber. For a Fabry-Perot intracavity saturable absorber with a highly reflecting back surface such as that considered here, it is often desirable to avoid the "etaloning" effect altogether by anti-reflection coating the surface facing the gain medium.
In general, however, R.noteq.0, and by choosing d and R appropriately, the loss of a Fabry-Perot saturable absorber can be effectively controlled. If the thickness of the saturable absorber is chosen to be a multiple integer of ##EQU1##
the device is said to be an anti-resonant Fabry-Perot saturable absorber (A-FPSA) (see U. Keller et al., "Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber," Opt. Lett., vol. 17, p. 505, 1992 and U.S. Pat. No. 5,237,577 to Keller et al.) In an A-FPSA, the side of the device facing the gain medium usually includes a high reflector. In this configuration, most of the incident light is the gain-medium-facing surface and little goes into the saturable absorber, thus reducing the light absorbed the saturable absorber. This low absorption design is appropriate for lasers with small output coupling and low single pass gain, such as solid state lasers. For example, if the laser has an output coupler of .about.4%, an insertion loss of nearly 0.5% may be desirable, which is lower than what is normally obtained from either a quantum well or bulk absorber semiconductor. Low loss A-FPSA devices have been used successfully in modelocked solid-state lasers (see, for example, U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, "Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber," Opt. Lett., 17, 505, 1992).
Other low loss designs have been successfully used in modelocking arrangements. For example, a quantum well saturable absorber can be inserted into a Semiconductor Bragg Reflector (SBR) (see U.S. Pat. No. 5,627,854 to Knox and also S. Tsuda, W. H. Knox, E. A. de Souza, W. Y. Jan, and J. E. Cunningham, "Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femto-second mode locking in solid state lasers," Opt. Lett., vol. 20, p. 1406, 1995). In this arrangement, light intensity decreases rapidly inside the SBR, and the insertion loss is controlled by precisely placing absorbing layers within the SBR.
Another means of manipulating the effective insertion and nonlinear losses is through appropriate positioning of the absorber in a standing wave. In this design, an incident beam is reflected by a high or partial reflector to form an intracavity standing wave in which the intensity varies between zero and twice the incident intensity. The insertion and nonlinear losses are controlled by appropriate positioning of absorbing layers within the standing wave electric field. In U.S. Pat. No. 5,701,327 to Cunningham et al., the quantum well absorption layers are inserted into a multiple half wavelength thick strain relief layer which is then deposited on top of an SBR. Since the total thickness of the strain relief layer is a multiple integer of half wavelengths a standing wave node is formed (where the intensity is minimum) at the surface facing the incident beam. This antiresonant design limits the amount of light going into the strain relief layer and hence limits the amplitude of the standing wave.
In another design (see U.S. Pat. No. 4,860,296 Chemla et al.), nonlinear loss is maximized by placing thin absorbing layers (separated by transparent spacers) at the antinodes of a standing wave to form a so called grating saturable absorber. By placing the absorbing layers at the antinodes, where the intensity is twice the average value, the nonlinear loss can be enhanced by up to a factor of 2 if the absorbing layers are very thin compared to the transparent spacers.
All of these prior art designs involve saturable absorbers having low insertion loss. Accordingly, the magnitude of the nonlinear loss is limited, being maximized when the saturable absorber is completely bleached. For a high gain, high output fiber laser, however, the magnitude of the nonlinear loss is preferably large for modelocking to be self-starting. On the other hand, the use of a highly nonlinear saturable absorber may lead to persistent Q-switching. Thus, there remains a need for saturable absorbers suitable for self-starting modelocking of high gain, high output lasers such as fiber lasers.